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A bstract We compute next-to-next-to-leading order perturbative corrections to the decay width difference of mass eigenstates and the charge-parity asymmetry a fs in flavour-specific decays of neutral B mesons. In our calculation we take into account the full dependence on the charm and bottom quark masses for the current-current operator contributions up to three-loop order. Special emphasis is put on the proper construction of the so-called |∆ B | = 2 theory such that Fierz symmetry is preserved. We provide updated phenomenological predictions, for ∆Γ, ∆Γ/∆ M and a fs for the B d and B s system, including a detailed analysis of the uncertainties of our predictions. The calculated NNLO correction reduce the perturbative uncertainty of the leading term of the 1/ m b expansion of the width difference ∆Γ s in the B s system to the level of the current experimental error. The uncertainty of our prediction ∆Γ s = (0.077 ± 0.016) ps − 1 is dominated by the sub-leading term of this expansion. We further illustrate how better future measurements of ∆Γ d and will help to gain a better understanding of mixing.

An important ingredient for the calculation of Higgs boson properties in the infinite top quark mass limit is the knowledge of the effective coupling between the Higgs bosons and gluons, i.e. the Wilson coefficients C H and C HH for one and two Higgs bosons, respectively. In this work we calculate for the first time C HH to four loops in a direct, diagrammatic way, discussing in detail all issues arising due to the renormalization of operator products. Furthermore, we also calculate the Wilson coefficient C H for the coupling of a single Higgs boson to gluons as well as all four loop decoupling relations in QCD with general SU( N c ) colour factors. The latter are related to C H and C HH via low-energy theorems, which are used to obtain five-loop results for the Wilson coefficients.

Modern advances in particle physics depend strongly on the usage of reliable computer programs. In this context two issues become important: The usage of powerful algorithms to handle the amount of evaluated data properly, and a software architecture capable of overcoming the problems of maintainability and extendability. We present our approach to such a computer program, called tapir. This tool assists computations in perturbative quantum field theory in many ways. Such calculations often involve the evaluation of a large amount of Feynman diagrams with multiple loops. tapir helps in reducing the number of diagrams, and the resulting integrals thereof, by identifying and minimizing their topological structure. We will focus on a three-loop calculation which is needed for the next-to-next-to leading order predictions of neutral B -meson systems. We show how tapir can be utilized for this kind of calculation.

A bstract We complete the calculation of the element Γ 12 q of the decay matrix in B q − B ¯ q mixing, q = d , s , to order α s in the leading power of the Heavy Quark Expansion. To this end we compute one- and two-loop contributions involving two four-quark penguin operators. Furthermore, we present two-loop QCD corrections involving a chromomagnetic operator and either a current-current or four-quark penguin operator. Such contributions are of order α s 2 , i.e. next-to-next-to-leading-order. We also present one-loop and two-loop results involving two chromomagnetic operators which are formally of next-to-next-to-leading and next-to-next-to-next-to-leading-order, respectively. With our new corrections we obtain the Standard-Model prediction ∆Γ s /∆ M s = (5 . 20 ± 0 . 69) · 10 − 3 if Γ 12 s is expressed in terms of the MS ¯ b-quark mass, while we find ∆Γ s /∆ M s = (4 . 70 ± 0 . 96) · 10 −3 instead for the use of the pole mass.

A bstract We consider two-loop QCD corrections to the element Γ 12 q of the decay matrix in B q − B ¯ q mixing, q = d, s , in the leading power of the Heavy Quark Expansion. The calculated contributions involve one current-current and one penguin operator and constitute the next step towards a theory prediction for the width difference ∆Γ s matching the precise experimental data. We present compact analytic results for all matching coefficients in an expansion in m c /m b up to second order. Our new corrections are comparable in size to the current experimental error and slightly increase ∆Γ s .

We complete the calculation of the element$$ {\\Gamma}_{12}^q $$Γ 12 q of the decay matrix in$$ {B}_q-{\\overline{B}}_q $$B q − B ¯ q mixing, q = d , s , to order α s in the leading power of the Heavy Quark Expansion. To this end we compute one- and two-loop contributions involving two four-quark penguin operators. Furthermore, we present two-loop QCD corrections involving a chromomagnetic operator and either a current-current or four-quark penguin operator. Such contributions are of order$$ {\\alpha}_s^2 $$α s 2 , i.e. next-to-next-to-leading-order. We also present one-loop and two-loop results involving two chromomagnetic operators which are formally of next-to-next-to-leading and next-to-next-to-next-to-leading-order, respectively. With our new corrections we obtain the Standard-Model prediction ∆Γ s /∆ M s = (5 . 20 ± 0 . 69) · 10 − 3 if$$ {\\Gamma}_{12}^s $$Γ 12 s is expressed in terms of the$$ \\overline{\\mathrm{MS}} $$MS ¯ b-quark mass, while we find ∆Γ s /∆ M s = (4 . 70 ± 0 . 96) · 10 −3 instead for the use of the pole mass.

We consider two-loop QCD corrections to the element$$ {\\Gamma}_{12}^q $$Γ 12 q of the decay matrix in B q −$$ {\\overline{B}}_q $$B ¯ q mixing, q = d, s , in the leading power of the Heavy Quark Expansion. The calculated contributions involve one current-current and one penguin operator and constitute the next step towards a theory prediction for the width difference ∆Γ s matching the precise experimental data. We present compact analytic results for all matching coefficients in an expansion in m c /m b up to second order. Our new corrections are comparable in size to the current experimental error and slightly increase ∆Γ s .

Abstract We complete the calculation of the element Γ 12 q$$ {\\Gamma}_{12}^q $$of the decay matrix in B q − B ¯ q$$ {B}_q-{\\overline{B}}_q $$mixing, q = d, s, to order α s in the leading power of the Heavy Quark Expansion. To this end we compute one- and two-loop contributions involving two four-quark penguin operators. Furthermore, we present two-loop QCD corrections involving a chromomagnetic operator and either a current-current or four-quark penguin operator. Such contributions are of order α s 2$$ {\\alpha}_s^2 $$, i.e. next-to-next-to-leading-order. We also present one-loop and two-loop results involving two chromomagnetic operators which are formally of next-to-next-to-leading and next-to-next-to-next-to-leading-order, respectively. With our new corrections we obtain the Standard-Model prediction ∆Γ s /∆M s = (5.20 ± 0.69) · 10 −3 if Γ 12 s$$ {\\Gamma}_{12}^s $$is expressed in terms of the MS ¯$$ \\overline{\\mathrm{MS}} $$b-quark mass, while we find ∆Γ s /∆M s = (4.70 ± 0.96) · 10−3 instead for the use of the pole mass.

Abstract We consider two-loop QCD corrections to the element Γ 12 q Γ₁₂^(q) of the decay matrix in B q − B ¯ q B̅_(q) mixing, q = d, s, in the leading power of the Heavy Quark Expansion. The calculated contributions involve one current-current and one penguin operator and constitute the next step towards a theory prediction for the width difference ∆Γ s matching the precise experimental data. We present compact analytic results for all matching coefficients in an expansion in m c /m b up to second order. Our new corrections are comparable in size to the current experimental error and slightly increase ∆Γ s .

A bstract An important ingredient for the calculation of Higgs boson properties in the infinite top quark mass limit is the knowledge of the effective coupling between the Higgs bosons and gluons, i.e. the Wilson coefficients C H and C HH for one and two Higgs bosons, respectively. In this work we calculate for the first time C HH to four loops in a direct, diagrammatic way, discussing in detail all issues arising due to the renormalization of operator products. Furthermore, we also calculate the Wilson coefficient C H for the coupling of a single Higgs boson to gluons as well as all four loop decoupling relations in QCD with general SU( N c ) colour factors. The latter are related to C H and C HH via low-energy theorems, which are used to obtain five-loop results for the Wilson coefficients.